Methods and apparatuses for versatile beamforming

The present invention is directed to methods and apparatuses for beamforming signals or compute beamformed signals. The present approach is to determine a series of beams from or for a set of devices configured for receiving signals from and/or transmitting signals to one or more regions of interest in an n-dimensional space, with n=2 or 3. Each of the devices has a known position pi within said n-dimensional space. Signals are to be respectively transmitted or received non-uniformly in this space, i.e., according to the particular regions of interest. During a first phase, operations are performed in order to successively obtain a spatial filter function {circumflex over (ω)}(r), a beamforming function ω(p), and beamforming weights ω(pi). The spatial filter function {circumflex over (ω)}(r) matches projections of the regions of interest onto an n−1-dimensional sphere centered on said set of devices. The function {circumflex over (ω)}(r), however, extends over the n-dimensional space and does not restrict to the n−1-dimensional sphere. During a second phase, delays and gains are suitably introduced in the signals, by weighting time-series according to beamforming weights ω(pi) obtained during the first phase.